The stabilizing encapsulation of a microbubble-based ultrasound contrast agent (UCA) critically affects its acoustic properties. Polymers, which behave differently from materials commonly used (i.e., lipids or proteins) for monolayer encapsulation, have the potential for better stability and improved control of encapsulation properties. Air-filled microbubbles coated with poly(DL-lactic acid) (PLA) are characterized here using in vitro acoustic experiments and several models of encapsulation. The interfacial rheological properties of the encapsulation are determined according to each model using attenuation of ultrasound through a suspension of microbubbles. Then the model predictions are compared with scattered non-linear (sub- and second harmonic) responses. For this microbubble population (average diameter, 1.9 µm), the peak in attenuation measurement indicates a weighted-average resonance frequency of 2.5-3 MHz, which, in contrast to other encapsulated microbubbles, is lower than the resonance frequency of a free bubble of similar size (diameter, 1.9 µm). This apparently contradictory result stems from the extremely low surface dilational elasticity (around 0.01-0.07 N/m) and the reduced surface tension of the poly(DL-lactic acid) encapsulation, as well as the polydispersity of the bubble population. All models considered here are shown to behave similarly even in the non-linear regime because of the low surface dilational elasticity value. Pressure-dependent scattering measurements at two different excitation frequencies (2.25 and 3 MHz) revealed strongly non-linear behavior with 25-30 dB and 5-20 dB enhancements in fundamental and second-harmonic responses, respectively, for a contrast agent concentration of 1.33 µg/mL in the suspension. Sub-harmonic responses are registered above a relatively low generation threshold of 100-150 kPa, with up to 20 dB enhancement beyond that pressure. Numerical predictions from all models show good agreement with the experimentally measured fundamental response, but not with the experimental second-harmonic response. The characteristic features of sub-harmonic responses and the steady response beyond the threshold are matched well by model predictions. However, prediction of the threshold value depends on estimated properties and size distribution. The variation in size distribution from sample to sample leads to variation in estimates of encapsulation properties: the lowest estimated value for surface dilational viscosity better predicts the sub-harmonic threshold.